Determine the mass of 3.16 ×1023 atoms Cl.
Answer in units of g.
How do you do this? Need to get it done really fast. Thanks for help.
1 mole of Cl has a mass of 35.5 approximately. Look it up to get the exact number. Then 1 mole of Cl atoms contains 6.02 x 10^23 atoms.
Ok, I got that, but what do I do with the 3.16 ×10^23?
What do you think? If 35.5 g Cl atoms contain 6.02 x 10^23 atoms, what is the mass of 3.18 x 10^23 atoms?
Totally lost.
If reasoning won't get it for you, set up a proportion.
mass/mass = #atoms/#atoms.
Is there anyway you could work this one out for me and explain what you did? I would probably learn a lot better than all of this reasoning and proportions. It's greatly appreciated.
OK but you aren't learning anything by me doing your work for you.
35.5 g Cl is the mass of 6.02 x 10^23 atoms. So 3.18 x 10^23 atoms will have a mass of ? grams.
Method 1. dimensional analysis:
3.18 x 10^23 atoms x (35.5 g/6.02 x 10^23 atoms) = 18.75 grams. Notice how the factor of (35.5 g/6.02 x 10^23 atoms) makes the unit come out right. You want grams. You have atoms. The unit atoms in the denominator of the fraction cancels with the unit atoms in the numerator and leaves the unit g alone. What we have done is convert atoms to grams. We canceled the unit we didn't want and kept the unit we wanted to keep. Technically, we should use two factors. One is that there are 6.02 x 10^23 atoms in a mole and 1 mole contains 35.5 g Cl.
So
3.18 x 10^23 atoms x (1 mole/6.02 x 10^23 atoms) x (35.5 g/mole) = 18.75 grams. Again, note that the unit of atoms cancels and the unit of mole cancels to leave grams. I show this "technical" step because you COULD reverse the atoms and come up with the wrong answer.
Method 2. ratio/proportion.
There are two or three ways of setting this up. I'll show you a couple.
mass/#atoms = mass/#atoms
35.5 g/6.02 x10^23 atoms = y g/3.18 x 10^23 atoms. Solve for y.
OR
mass/mass = #atoms/#atoms
35.5 g/y g = 6.02 x 10^23 atoms/3.18 x 10^23 atoms. Solve for y.
You should get the same answer of 18.75 no matter which of the three you prefer. You should look up the atomic mass of Cl and use that instead of my 35.5 which I'm using from memory. Also, I've used 4 significant figures in the 18.75 and I'm not allowed but 3 so it should be rounded to 18.8 g if the 35.5 is ok.